One of the juicier nuggets in TIME’s wide-ranging new poll is that voters are embracing the Occupy Wall Street movement as they sour on the Tea Party. Twice as many respondents (54%) have a favorable impression of the eclectic band massing in lower Manhattan’s Zuccotti Park than of the conservative movement that has, after two years, become a staple of the American political scene.

A closer look at the poll’s cross-tabs provides a fuller picture of the movement’s diverse support. Occupy Wall Street enjoys majority backing among men (57%) and women (51%), young (60% of respondents 18 to 34) and old (51%). Self-identified Democrats, unsurprisingly, comprise the left-leaning movement’s largest bloc, with 66% professing support. But more than half of independents (55%) harbor favorable views of the protesters, as do a third of Republicans.

As the movement has snowballed, it has become — as the Tea Party did — the subject of sneers from opponents bent on undermining its objectives and minimizing its influence. Like the Tea Party, it benefits in its incipient stages by venting a broad array of common frustrations. Many of these are vague enough that even Republicans can co-sign them. Of the respondents in TIME’s poll familiar with the protests, 86% — including 77% of Republicans — agree with the movement’s contention that Wall Street and its proxies in Washington exert too much influence over the political process. More than 70%, and 65% of Republicans, think the financial chieftains responsible for dragging the U.S. economy to the brink of implosion in the fall of 2008 should be prosecuted. Other questions reveal a sharper split along partisan lines but nonetheless reveal the strength of economic populism. Nearly 80% of respondents (96% of Democrats and 56% of Republicans) think the class chasm between rich and poor has grown too large, and 68%, including 40% of Republicans, say the affluent should pay more taxes.

There are warning signs embedded in the good news too. Not the least of these is the Tea Party’s own waning influence. That grassroots movement also grew from the seeds of economic frustration, generalized rage at Washington’s policies and a virulent strain of populism. Over time, those broadly popular sentiments calcified into a hard-line movement that regards political cooperation as grounds for a primary challenge. TIME’s poll provides a snapshot of a movement that no longer boasts the broad support it once enjoyed. Just 34% say the Tea Party has had a positive impact on U.S. politics, including just 35% of independents. Only 11% of respondents familiar with the movement call themselves members. It’s easy to trace the Tea Party’s withering support to its obstinacy; 89% of those surveyed argue that it’s better for politicians to find common ground than to be hidebound to fixed principles.

To avoid the same fate as it matures, Occupy Wall Street will have to do a better job than the Tea Party of negotiating that tightrope between principle and pragmatism. The swelling movement will have to clarify its goals, contend with Establishment forces seeking to co-opt its enthusiasm and confront the reality of a gridlocked Congress. The Tea Party backlash came only after it made that gridlock worse. For Occupy Wall Street, channeling early momentum into staying power won’t be easy, and both sides know it: 56% of respondents, including 51% of Democrats and 53% of the 18-to-34 demographic that forms the movement’s backbone, say it will ultimately have little impact on U.S. politics. The protesters’ challenge is to prove them wrong.